We propose a penalized likelihood method that simultaneously fits the multinomial logistic regression model and combines subsets of the response categories. The penalty is nondifferentiable when pairs of columns in the optimization variable are equal. This encourages pairwise equality of these columns in the estimator, which corresponds to response category combination. We use an alternating direction method of multipliers algorithm to compute the estimator and we discuss the algorithm’s convergence. Prediction and model selection are also addressed. Supplemental materials for this article are available online.
Bibliographical noteFunding Information:
This research is partially supported by the National Science Foundation grant DMS-1452068. The authors thank the referees and the associate editor for helpful comments.
© 2019, © 2019 American Statistical Association, Institute of Mathematical Statistics, and Interface Foundation of North America.
- Fusion penalty
- Multinomial logistic regression
- Response category reduction